Find Angle BAD in a Quadrilateral with Given Angles 71°, 95°, and 120°

Q: Why is the angle sum 360° and not 180° like triangles?

A quadrilateral can be divided into two triangles by drawing a diagonal. Since each triangle has angles summing to 180°, the quadrilateral total is 2 × 180° = 360°!

Q: Do all quadrilaterals follow this 360° rule?

Yes! Whether it's a square, rectangle, trapezoid, or any irregular quadrilateral, the interior angles always sum to exactly 360°. This is a fundamental geometric property.

Q: What if the quadrilateral looks weird or irregular?

The shape doesn't matter! As long as it's a four-sided polygon, the angle sum rule applies. Even if sides cross or the shape is concave, interior angles still sum to 360°.

Quadrilateral Angle Sum with Missing Angles

The quadrilateral ABCD is shown below.

Calculate the size of angle $∢\text{BAD}$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find angle B, A, D.

00:09 Remember, the sum of angles in any quadrilateral is 360 degrees.

00:18 Plug in the given values, and solve step by step to find our missing angle.

00:35 Next, focus on isolating angle A.

00:49 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The quadrilateral ABCD is shown below.

Calculate the size of angle $∢\text{BAD}$ .

Step-by-step solution

To find the measure of angle $∢\text{BAD}$ in quadrilateral $ABCD$ , we apply the formula for the sum of interior angles of a quadrilateral:

The sum of the interior angles in any quadrilateral is $360^\circ$ .
Therefore, we have the equation: $∢\text{BAD} + 71^\circ + 95^\circ + 120^\circ = 360^\circ$ .

Solving for $∢\text{BAD}$ :

Add the given angles: $71^\circ + 95^\circ + 120^\circ = 286^\circ$ .
Subtract the sum from $360^\circ$ : $360^\circ - 286^\circ = 74^\circ$ .

Therefore, the measure of angle $∢\text{BAD}$ is $\boxed{74^\circ}$ .

The correct answer to the problem is $\boxed{74}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: All quadrilateral interior angles sum to exactly 360°
Technique: Add known angles: 71° + 95° + 120° = 286°
Check: Verify sum: 74° + 71° + 95° + 120° = 360° ✓

Common Mistakes

Avoid these frequent errors

Forgetting that quadrilaterals have 360° total
Don't assume quadrilaterals follow the triangle rule of 180° = wrong answers like 180° - 286° = impossible! This fundamental error ruins the entire calculation. Always remember quadrilaterals sum to 360°, not 180°.

Practice Quiz

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Can a triangle have a right angle?

FAQ

Everything you need to know about this question

Why is the angle sum 360° and not 180° like triangles?

A quadrilateral can be divided into two triangles by drawing a diagonal. Since each triangle has angles summing to 180°, the quadrilateral total is 2 × 180° = 360°!

What if I get a negative number when subtracting?

If your calculation gives a negative result, you've made an error! Check that you're using 360° for quadrilaterals, not 180°. Also verify you added the given angles correctly.

Do all quadrilaterals follow this 360° rule?

Yes! Whether it's a square, rectangle, trapezoid, or any irregular quadrilateral, the interior angles always sum to exactly 360°. This is a fundamental geometric property.

How can I double-check my arithmetic?

Add your answer to the three given angles. The total should equal 360°. In this problem: 74° + 71° + 95° + 120° = 360° ✓

What if the quadrilateral looks weird or irregular?

The shape doesn't matter! As long as it's a four-sided polygon, the angle sum rule applies. Even if sides cross or the shape is concave, interior angles still sum to 360°.

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